OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).
FORMULA
Coefficient of x^(n^5) in 1/((1-x)*(1-x^2)).
a(n) = A008619(n^5).
a(n) = (3 + (-1)^n + 2*n^5)/4.
a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7) for n > 6.
G.f.: (1 - 4*x + 21*x^2 + 41*x^3 + 46*x^4 + 15*x^5) / ((1-x)^6*(1+x)).
E.g.f.: ((2 + x + 15*x^2 + 25*x^3 + 10*x^4 + x^5)*cosh(x) + (1 + x + 15*x^2 + 25*x^3 + 10*x^4 + x^5)*sinh(x))/2. - Stefano Spezia, Mar 17 2024
MAPLE
MATHEMATICA
Table[(3+(-1)^n+2*n^5)/4, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 25 2016 *)
PROG
(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)).
b(n) = (3+(-1)^n+2*n)/4
vector(50, n, n--; b(n^5))
(Magma) [(3+(-1)^n+2*n^5)/4 : n in [0..50]]; // Wesley Ivan Hurt, Jun 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 18 2016
STATUS
approved